Lloyds Banking Group will float TSB at up to 30pc below its book value in an attempt to engineer a smooth sale of the challenger bank.

The taxpayer-backed lender, which is selling off TSB as a condition of its 2008 government bailout, has priced it at between 220p to 290p a share.

This will value it at between £1.1bn and £1.45bn, or between 0.7 and 0.9 times its book value. Lloyds, which will float the minimum possible 25pc of TSB at the end of the month, is pricing the bank at a level that it hopes will ensure a clean sale amid waning investor appetite for initial public offerings.

Both Saga, the over-50s holidays and insurance group; and Game Digital, the computer games retailer; priced their recent IPOs at the bottom of their ranges, and the vast majority of companies to list this year are now trading at below their float price.

However, on Monday night it emerged that the offer had been fully subscribed. Lloyds will announce pricing around June 20.

Lloyds, 25pc owned by the taxpayer, must sell off branches under European state support rules. It had originally agreed to sell 631 branches to the Co-operative Bank for £750m, but the deal collapsed shortly before a £1.5bn black hole in the Co-op Bank emerged. This led to the revival of TSB as a high street name last year, almost two decades after Lloyds and TSB merged in 1995.

Lloyds must sell the whole of TSB by the end of next year, and is determined to ensure a successful flotation. Royal Bank of Scotland, which was ordered to sell its Direct Line insurance business under the same rules, disposed of the business in four episodes, each time at a higher level than before.

TSB’s prospectus revealed adjusted profits of £172m last year, up from £28m in 2012. In the first three months of 2014, it made an adjusted profit of £60m.

The bank is positioning itself as a growth stock, claiming its low share of current accounts compared to its branch network means it will be able to grab more customers. It plans to invest £250m over the next five, including on opening new branches, and does not plan to pay a dividend until 2017.

Lloyds was one of the biggest fallers on the FTSE 100 on Monday, dropping 1.7pc to 78.8p.